Your blood pressure increases in the fight or flight response, due to the constriction of blood vessels and the increase in your heart rate and increase in heart contractions. The increase in blood pressure insures that there is increased blood flow to the skeletal muscles and your brain, when you have the fight or flight response triggered. This ensures adequate oxygenation and fuel (glucose) to your muscles and brain so that your body can prepare itself to either fight the danger or to run from it.
The following video explains how the fight or flight response works:
